Bessel potentials in Orlicz spaces.

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It is shown that Bessel potentials have a representation in term of measure when the underlying space is Orlicz. A comparison between capacities and Lebesgue measure is given and geometric properties of Bessel capacities in this space are studied. Moreover it is shown that if the capacity of a set is null, then the variation of all signed measures of this set is null when these measures are in the dual of an Orlicz-Sobolev space.

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@article{Aïssaoui1997, abstract = {It is shown that Bessel potentials have a representation in term of measure when the underlying space is Orlicz. A comparison between capacities and Lebesgue measure is given and geometric properties of Bessel capacities in this space are studied. Moreover it is shown that if the capacity of a set is null, then the variation of all signed measures of this set is null when these measures are in the dual of an Orlicz-Sobolev space.}, author = {Aïssaoui, N.}, journal = {Revista Matemática de la Universidad Complutense de Madrid}, keywords = {Potencial de Bessel; Espacio de Orlicz; Espacio de medida; Representaciones; Bessel potentials; representation in term of measure; Lebesgue measure; Bessel capacities; signed measures; Orlicz-Sobolev space}, language = {eng}, number = {1}, pages = {55-79}, title = {Bessel potentials in Orlicz spaces.}, url = {http://eudml.org/doc/44245}, volume = {10}, year = {1997},}

TY - JOURAU - Aïssaoui, N.TI - Bessel potentials in Orlicz spaces.JO - Revista Matemática de la Universidad Complutense de MadridPY - 1997VL - 10IS - 1SP - 55EP - 79AB - It is shown that Bessel potentials have a representation in term of measure when the underlying space is Orlicz. A comparison between capacities and Lebesgue measure is given and geometric properties of Bessel capacities in this space are studied. Moreover it is shown that if the capacity of a set is null, then the variation of all signed measures of this set is null when these measures are in the dual of an Orlicz-Sobolev space.LA - engKW - Potencial de Bessel; Espacio de Orlicz; Espacio de medida; Representaciones; Bessel potentials; representation in term of measure; Lebesgue measure; Bessel capacities; signed measures; Orlicz-Sobolev spaceUR - http://eudml.org/doc/44245ER -